1. Field of the Invention
This invention relates to controllers of the type known as self-tuning or automatic-tuning and more particularly to a method and apparatus for use in such controllers to obtain the process characteristics.
2. Description of the Prior Art
Industrial processes are typically overdamped and of higher-order having two or more poles. In addition, a typical industrial process has one pole that is more dominant than the other poles. It is for this reason that various methods have been used for many years to approximate a higher-order industrial process by a first-order (single pole) system with pure time delay.
Often an open loop step response is used to obtain the characteristics of the process. An open loop step refers to the process controller (independent of the process reaction) outputting a sudden change in constant signal level to the process. A step input to the process is equivalent to applying the entire spectrum of frequencies to the process; hence, the process response to the step depends on its dynamic characteristics. An open loop step response is a good way to analyze the process.
It has been known for many years that the overall deadtime and time constant of an industrial process are closely related to the optimum proportional, integral and derivative ("PID") values of the controller which is to control it. This relationship is described in "Optimum Settings for Automatic Controllers", J. G. Ziegler and N. B. Nichols, Transaction ASME, 64, pp. 759-765 (1942). Ziegler and Nichols refer to deadtime rather than overall deadtime and it is not clear to me if their deadtime is the same as overall deadtime; in the sense that overall deadtime is the sum of the "apparent delay" and the "transport delay". The apparent delay and the transport delay will be defined hereinafter in connection with the description of FIG. 7. The discussion which follows herein assumes that the Ziegler-Nichols deadtime is the same as the overall deadtime.
Ziegler and Nichols suggest that a tangent line should be drawn where the slope is maximum on the open loop step response curve (the "Ziegler-Nichols method"). For many years the only way to implement the Ziegler-Nichols method was to plot the response on paper and draw the tangent line on the plot. The point where the tangent line intercepts the time axis is defined as the end of the overall deadtime for the process. Hence, the time from the relative starting point to this slope intercept of the time axis equaled the overall deadtime.
A second method that was considered at the time it was published to be an improvement over the Ziegler-Nichols method, is described in "A Comparison of Controller Tuning Techniques", J. A. Miller, A. M. Lopez, C. L. Smith, and P. W. Murrill (the "Miller, et al. method"), Louisiana State University, Control Engineering, Dec. 1967, pp. 72-75. The Miller, et al. method determines overall deadtime the same way as the Ziegler-Nichols method does. However, the Miller, et al. method defines the time constant as the difference in time between where the step response reached 63.2% of its final value and the overall deadtime. This sounds easy to implement, but it will be shown later that it is not practical to implement in a self-tuning controller.
Miller, et al. state that the difference between the starting level and where the maximum slope intercepted the vertical axis should be considered in the Ziegler-Nichols method to be the ratio of the overall deadtime to the time constant. Therefore, in the Ziegler-Nichols method the time constant equals the overall deadtime divided by the ratio of overall deadtime to time constant. Another way to view it is that in the Ziegler-Nichols method the time constant is inversely proportional to the maximum slope of the response.
The arrival of microprocessor based controllers allowed the process approximation methods to be automated. The automated process approximation methods can be used to arrive at the optimum proportional, integral, and derivative constants for PID controllers. PID controllers are well known in the art and many extensive studies have been done to relate the optimum PID constants to the ratio of overall deadtime and time constant of a first-order system. This is the motivation for accurately matching an industrial process to a first-order system. The results for this optimum PID relationship are very different depending on the criteria the study is based on. Therefore, the present invention is not concerned with which set of criteria is best, but rather, it concentrates on the optimum fitting of a first-order approximation with delay to a real industrial multi-order process open loop step response. The objective is that in order to apply the optimum PID criteria, one must first have the optimum first-order approximation of the process to start with. Controllers of this type that analyze the process and calculate their optimum PID values automatically are commonly referred to as self-tuning or automatic-tuning controllers.
There are other process approximation methods in addition to and more recent than the Ziegler-Nichols and Miller, et al. methods described above. One such method is described in U.S. Pat. No. 4,602,326 (Kraus) wherein a controller outputs a step to the process which increases the magnitude of the process control variable from its steady state value of N to a new level that is 10% above N. In one embodiment the method described in Kraus uses a starting point (T.sub.f of FIG. 9 of Kraus) which occurs 15 seconds prior to the output step. The controller records the time of occurrence at which the process control variable has increased in magnitude by 1%, 2%, 3% and 4% above its steady state value of N. In addition, the controller finds the upper inflection point by a technique referred to in Kraus as the chord method. Slope is measured from the inflection point to each of the one percent increase in magnitude occurrence points. The method chooses the one percent point which has maximum slope and assigns a line from the inflection point to that point. The intersection of that line with the x axis (which is representative of time) is considered to be the overall deadtime of the process. In this respect the method taught by Kraus is identical to the previously described Ziegler-Nichols method.
Another method, described in U.S. Pat. No. 4,881,160 (Sakai, et al.), is said to be an improvement over the chord method described in Kraus. The method described in Sakai, et al. to determine slope uses six points to find five gradients (see FIG. 19 of Sakai, et al.). A correction factor is applied which appears to assume only a first-order response. This is one of the drawbacks of the method described in Sakai, et al. It is well known that industrial process step responses are more representative of second-order or higher-order responses. The correction factor and added points of Sakai, et al. may very well be an improvement over the chord method described in Kraus; however, both the Kraus and Sakai, et al. methods are still inferior when compared to the present invention.